There are others who argue that probability is properly applied only to random events as outcomes of some specified random experiment, for example sampling from a population; this is the frequentist interpretation.

There are several other interpretations which are variations on one or the other of those, or which have less acceptance at present.

He can't decide whether this is just a random event—after all, it is possible (although unlikely) that a fair coin would give this result—or whether his assumption that the coin is fair is at fault.

If a randomvariable is uniformly distributed, that means that the probability of landing in a particular interval is equal to the size of that interval divided by the size of the entire distribution.

In general, the expected value of a randomvariable, written as E(X), is equal to the weighted average of the outcomes of the randomvariable, where the weights are based on the probabilities of those outcomes.

A randomvariable is not a variable in the same sense the word is used in calculus or algebra: It is something that takes a random value, depending on the outcome of a random experiment.

The number of random draws with replacement from a 0-1 box until the first time a ticket labeled "1" is drawn is a randomvariable with a geometric distribution with parameter p=G/N, where G is the number of tickets labeled "1" in the box and N is the total number of tickets in the box.

Even though the randomvariable X counts "successes" in a fixed number (four) of independent trials, it does not have a binomial probability distribution, because the probability of success is not the same in every trial: It is 1/2 in the trials that involve the coin, and 1/6 in the trials that involve the die.

A discrete randomvariable, x, occurs with probability f(x) and is an element of the finite or countably infinite set of all possible events X.

A continuous randomvariable is defined for some interval on the line of real numbers; but the probability that a continuous randomvariable, x, takes on any specified real value in the interval is equal to zero.

The normal, or Gaussian, distribution is widely applicable as a probability model for continuous randomvariables that may be thought of as resulting from the sum of a large number of small effects.

mcardle.oncology.wisc.edu /mstat/Mhelp/StatNotes-3.html (4656 words)

Lost causes in physics, by R. F. Streater(Site not responding. Last check: 2007-10-10)

By allowing that the randomvariable chosen by A to model X if B measures Y to be a different randomvariable from the one she chooses if Bob measures Z, one can reproduce the quantum correlations exactly.

The representation of the observables as randomvariables is, in each case, then an immediate consequence of Gelfand's general construction of a representation of a commutative C* sub-algebra by bounded randomvariables defined on the spectrum of the subalgebra.

He relaxed the requirement that the quantum algebra be irreducible, and was able to find a class of homomorphic mappings from the Poisson algebra to the algebra of linear operators on the space of smooth functions on phase space.

www.mth.kcl.ac.uk /~streater/lostcauses.html (12381 words)

Course Listing For STAT(Site not responding. Last check: 2007-10-10)

Types of sampling and types of statistical studies; basic, probability, randomvariables and their distribution, specific discrete and continuous distributions producing models using probability and simulation; summarizing and exploring data using graphical techniques and numerical summaries; exploring and making inferences for relationship between two variables: contingency tables, chi-sq.

The material in this section represents a synthesis of these various frameworks emphasizing those aspect that are most directly related to the formulation of the stochastic finite element method.

P ; H;F H) In this notation, H specifies the Gaussian subspace of randomvariables with which events in the algebra FH are associated, while the algebra F H contains the events that are independent of H, and is referred to as the transverse oe algebra or the algebra of transverse events

The oe algebra, F, of all randomvariables is then given by the tensor product F = FH Omega F H ; 5) indicating that an arbitrary event could involve combinations of events associated with H and others that are not.

Conditional event algebra (CEA) was developed in order to represent conditional probabilities with differing antecedents by the probability evaluation of well-defined individual "conditional" events in a single larger space extending the original unconditional one.

A major application of CEA is to data fusion problems, especially the testing of hypotheses concerning the similarity or redundancy among inference rules through use of probabilistic distance functions which critically require probabilistic conjunctions of conditional events.

Relational event algebra (REA) is a further extension of CEA, whereby functions of probabilities formally representing single event probabilities - not just divisions as in the case of CEA - are shown to represent actual "relational" events relative to appropriately determined larger probability spaces.

quanterion.com /Documents/Documents.asp?ArgVal=336 (292 words)

Means and variances of random variables(Site not responding. Last check: 2007-10-10)

Topics include: descriptive statistics, probability, randomvariables and distributions, sampling distributions of sample mean and proportion, statistical inference for population mean and proportion for single sample, comparison of two population means and proportions, simple linear regression, and introduction to multiple regression.

Because the career objectives of undergraduate mathematics majors are so diverse, each undergraduate's program is individually arranged through collaboration between the student and his or her faculty advisor.

In general, students are encouraged to explore the various branches of mathematics, both pure and applied.

Various MIT faculty are openly sharing these resources as a service to MIT OCW users.

ocw.mit.edu /OcwWeb/Mathematics (371 words)

Exact Analysis of Postdetection Combining for DPSK and NFSK Systems Over Arbitrarily Correlated Nakagami Channels(Site not responding. Last check: 2007-10-10)

The difficulty arises from inherent nonlinearity in noncoherent detection and from attempts to determine explicitly the probability density function of the total signal-to-noise ratio at the combiner output.

Curland, "Distribution of the maximum of the arithematic mean of correlated randomvariables," Ann.

Week three: Events and randomvariables; mutual exlusiveness and independence of events; difference between independence of events and independence of randomvariables (the local minimum problem in homework one); conditional probability (the filp-coin problem in homework one); review of linear algebra continued (if time allows).

SHAPE AND GEOMETRY (3) Younes Prereq: Calculus III and Linear Algebra This class will review the basic definitions and properties of curves and surfaces, and their relation to the description and characterization of 2D and 3D shapes.